Because the trajectory of light is only altered at the input and the output surfaces of a conventional lens, and left to travel in a straight line within the volume of the lens, it is difficult to create as ideal an optical device as one would desire. Monochromatic aberrations, such as spherical or coma, are generally unavoidable with refractive optics and can at best be minimized through the use of systems of many lenses. The aberration profiles of lenses place an ultimate limit on certain high-performance imaging applications. Wide-angle imaging systems, for example, make use of stacks of lenses, yet often exhibit significant distortion even after optimization.
Gradient index lenses represent an alternative approach to lens design. Rather than relying on the interfaces of a uniform material to manipulate light, the index of refraction is varied throughout the body of the lens. Rays are no longer abandoned once entering the medium, but instead can be guided with far greater control to their ultimate destination. For instance, it has long been known that it is possible to create a gradient index lens with no geometrical aberrations, which focuses rays incident from infinity to the surface of a sphere. Such a lens is called a Luneburg lens, after the inventor.
Gradient index lenses are typically composed of inhomogeneous materials in which the index-of-refraction varies spatially throughout the volume of the medium. The Maxwell “fish eye” lens is a second example of this class of lenses, which achieve their function via a complicated, inhomogeneous medium as opposed to refractive lenses, which rely on engineering the interfaces between two mediums whose refractive indices differ. Though the Luneburg and the Maxwell “fish eye” and similar gradient index lenses have considerable advantages, such as wide field-of-view or significantly reduced geometrical aberration profiles, the particular well known examples typically have focal regions that lie on curved surfaces rather than planes, which is generally incompatible with the planar geometry of virtually all charge coupled device (CCD) arrays used to acquire images. In addition, the process of achieving large index gradients in a controlled manner poses a difficult fabrication challenge. For these reasons, these lenses have found only limited commercial success.
Because lenses such as the Luneburg or the Maxwell fish eye have such favorable imaging characteristics, however, it is of interest to develop a design that can render these gradient index devices more feasible for applications.